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This was indeed a very interesting project and puzzle to solve. I used the Piano Rebuilder’s Handbook of Treble String Tensions (and Other Characteristics) compiled by James H. Donelson RPT, published in 1977. It is a table of numbers that I used to rescale over 20 pianos back in the late 1980’s and early 1990’s.

What I gathered about the piano you are working with is that it has some unusually long speaking lengths in its hi-mid and low treble sections. Therefore, smaller than usual wire is recommended than for most pianos in these areas (as BDB pointed out in contradiction to what the Klepac chart suggests). Also, at the very top, the speaking lengths were slightly long and could have even used some #12 and #12 ½ wire but with the size #13 and #13 ½ wire that I suggested, the tensile strength lies still well below the maximum of 70% which is recommended. I have seen many scales with even higher tension in this area.

The “%tensile” figures indicate the percentage of tension at theoretical pitch before the string would break. Since most people will tune these highest strings considerably sharper than that, one would certainly not want to exceed the 70% limit. Although I did not look up what size #14 would have provided in the areas where I suggest #’s 13 & 13 ½, I can well imagine that the tension would have been dangerously high. These wire sizes will also produce a good, strong sound whereas #’s 12 & 12 ½ may sound a little on the weak side. It is normal for most scales to have slightly higher tension in the highest part of the high treble.

The Inharmonicity column indicates the amount of difference between the 1st and 2nd partials, (one octave higher than the fundamental). You will note that the 4 highest strings have 1st partial inharmonicity of over ¼ of a step. This is normal in this area of the piano but if size #14 wire had been used, the inharmonicity would have been all the more exaggerated.

From the notes 80 all the way down to 30, I was able to keep the average tension hovering around 150 pounds as BDB has suggested. This should provide you with a light sounding and easy to tune piano with relatively low inharmonicity compared to many others. Only at the lowest end does the inharmonicity start to climb again but just very slightly. Also, at the lowest end, any wire size above #19 would tend to sound very loud and brassy, this is the reason for dropping back to a bichord (2 string unison). You will notice in looking at the figures, in spite of increasing dramatically the size or wire, the pounds of tension and % tensile drop off precipitously but the inharmonicity rises slightly. This is entirely due to insufficient speaking length and why some kind of compromise is called for. If #19 wire were used in this area, the tension would drop very low indeed and tunings would be very unstable in this area, responding dramatically to the least rise and fall in relative humidity. The tone would also be weak and “wolfish” sounding.

Do not be alarmed by the words “estimate” you see beginning at note 62 and below. This certainly does not mean I merely estimated which wire size should be there. The very fine measurements you took from notes 62 and below sometimes fell in between the figures that are in the table I have. The author noted that these fine increments were passed over to keep the table of figures from being too cumbersome since such small increments make literally no difference in determining which wire size to use in this area.

However, if one uses a computer spreadsheet and calculations, having such small distinctions does make for an even smoother looking curve. Therefore, I estimated what those figures would be for you. The estimates are merely the very insignificantly small differences in tension, % tensile and inharmonicity. If I had used either the next fraction up or down, it would have made no difference whatsoever in the choice of wire size.

I noted that you identified C4 as C3 but I corrected that in the chart you offered. I placed asterisks (***) to help the figures I supplied line up better so you could more easily see the curves of all four characteristics: wire size, pounds tension, % tensile and inharmonicity.

You will notice that at note #68, I made the notation “back-up/break”. I assume this is the break between the high treble and the treble. In many pianos, the bridge goes straight across this break but I imagine that on your piano, the bridge continues to curve. Therefore, there is a noticeable “jump” in length between notes 68 & 67, which calls for a smaller wire size. So, the pattern of wire sizes takes a step back from 14 ½ to 14 which is unusual, virtually never seen in finer pianos. But in this case, it provides for the smoothest curve possible. I have done this a number of times before on smaller, lesser quality pianos. Trust me; it is an improvement, not a mistake in judgment.

Only down at notes 31 and below do I run into a dilemma. I imagine this is where the bridge takes a “left turn” and creates the “hockey stick” appearance. The speaking lengths increase very little for each successive note when they should increase a whole inch or so for plain wire to be effectively and best used this low in a scale. This is where specially designed wound strings would best be used but that would require adding hitch pins, replacing agraffes with 2-string types, etc. So, where you see the words, “bichord”, simply guide your plain wire through the outside holes in the agraffes and bridges and leave the centers blank. Put in a tuning pin in the center hole but just leave it blank. If in the end, you don’t like the outcome, you can always use size #19 to the bottom, possibly putting size #20 on the lowest, tied off unison.

It is unfortunate that you must buy some sizes of wire for only one or two unisons. Just buy the smallest quantity you can for those sizes. Also, you’ll note that I skipped size #18 wire entirely. This is just how it worked out. I also used size 19 ½ and 20 ½ wire when most pianos skip half sizes anywhere past size #18. Again, this was the best compromise. You certainly can choose to use size #19 from note 32 all the way down using 3 string unisons if you so choose. Many pianos are built this way and apparently so was this one. The compromise I offer is in my opinion a better solution, however.

I started by looking at a scale around 140 lb., but saw that there would be a problem with the lowest plain string. So I went with a linear increase from 125 lb. up to about 150 lb. at the top. I was not willing to share a hitchpin between two different gauges of wire, and took an average when necessary. The result actually goes from about 108 lb. to about 160 lb.

So it is a little lower tension than Bill's, and it is not terribly different from other scales, except that the area where the gauges stay constant are higher than is traditional. There are not any sizes skipped, other than half sizes in the tenor, which is traditional. It uses the existing hitchpins as it was designed. So it is a reasonable scale, which will not throw someone else who works on it.

I noticed also that the area where there are many of the same size wire in a row was higher than usual too. This usually occurs in the #17 wire size area. I have done the sharing of two wire sizes on one hitch pin a few times. I found it was possible to put two strings together and create a single tie-off with them, for example. In one instance of an older Baldwin grand, I hid the splice between two strings beneath the string braid. I didn't find these kinds of tricks necessary in this case, however.

The conversion or the lowest tenor strings to wound bichords is commonly done these days. Sometimes, a rebuilder fills in the center tuning pin hole and finishes over it. The wire sizes need to be marked on the piano one way or the other such as a neatly written number on the plate by the tuning pins or on the bridge itself. I used to use number decals that I bought at an art store. I don't really see the minor alterations I suggested as being a problem for anyone. If a string should break and it needs to be replaced but the wire gages are plainly marked, there should be no question about what goes where. While plain wire bichords in the low tenor may surprise someone who has never seen such an alteration before, even a visually impaired person can easily detect which wire goes to a pin and that there are only two strings, not three.

Some scales do skip wire sizes but they are usually whole sizes past #18. In this case, some of the higher half sizes worked out better. I noted that BDB used only one #18 but also that the original also skipped that size.

-12 Unisons of sz. 17 1/2-5 Unisons of sz. 17-3 Unisons of sz. 19

I would not insist upon, just recommend the bichords and the sizes I suggested. For the lowest 3 notes, the original design of 3 #19 would not be very good. However, I would say that what BDB suggested:

Roughly speaking:

1 - 212 - 202 - 19

...would also be quite reasonable and could also use 3 string unisons without skipping any holes or hitch pins. But these 3 lowest notes would be quite loud and brassy sounding, so very aggressive hammer voicing would be called for, especially for the very lowest note. Another alternative could be to make only that lowest note a bichord, skipping the last hitch pin (but using #21 wire, not #22). These lowest strings would still have extremely low tension however and would have more trouble staying in tune but not as much and as extremely so as the original design, just in between what I suggested and the original.

I'll take back the comment I made about making a composite. I think substituting BDB's idea for the lowest 5 notes as I mentioned above is a perfectly reasonable idea. I just think it's important to consider all the benefits and consequences. While I don't see a problem with the conversions/alterations I suggest, BDB seems to think there is that possibility. So, in the end, Ryan the final decision will be up to you but whatever decision you make, there is always the possibility of changing it. None of what was proposed by either of us will lead to a point of no return.

One final comment I would have about the original design: the large number of 17 and 17.5 wires are in the usual area that they occur except that the sizes are curiously reversed (unless Ryan mistakenly listed them that way). This would in this case however, be very poor design indeed. The tension would go from extremely low to very high and then back to low again, so would the volume and so would the inharmonicity except in the lowest strings where it would remain about as high or higher than in my design. I don't know what any of the figures would be for note 27 (B2) with #19 wire because that is considered so unreasonable as to be off the chart! No calculated ETD program could deal with it very well at all.

I doubt Ryan measured the original wires correctly. It is not easy to do even if you are skilled with the use of a micrometer. Sometimes you have to look more for changes, than accurate measurement, and base it on your knowledge of past scaling practices. The numbers Ryan gave were so at odds with those practices that I never considered that they were accurate.

I have also considered that it is possible he has not measured the lengths as accurately as I might like. I am more certain that the scale design was not particularly good. If I were to consider changing hitchpins, I would probably use overwound strings on the lowest 5 notes. But this piano is probably not worth the effort.

I also suspect that the lowest notes will not be ideal. But I bet they would be better than they were originally. It is probable that the lowest strings were thinner than either Bill or I suggested, which would mean that they would have very low tension. (If the piano has agraffes, make sure the holes in them are big enough! You may need to ream them.) So whatever you do is likely to be an improvement.

I reingineered the strings of an old 1895 Sohmer Grand (original strings) using the Travis book. Took me all day but I think it was worth it. A few observations: Most of the original string gagues were beyond their flexibility for the note they were supposed to produce at that length given the necessary tension required, therefore the wrong strings (possibly due to A435 original calculations versus A440); My range ended up being much greater, starting with 11 at the top instead of 12, and 22 at the bottom instead of 20; I also added several half steps in string sizes that were not originally there; Note that when old strings stretch they are actually thinner in the middle of the string than toward the ends - so measuring near the far ends are closer to the original size; I found a cheap electronic tape measure online for about $14 that had decimal places for measuring; I think next time I will use the excel spreadsheet, but cross reference it against the Travis scale to make sure they are within flexibility range; The Travis book does not work on the bass strings so make sure you send the last string length and diameter to the base string company so they can make a smooth transition between the bass strings and the treble; Some pianos have a crooked bridge, I assume to make some compensation, but the tension must vary in an odd way, as I have seen several later Sohmer pianos (1930-1940) with cracks in the sound board near the crook.

Wire strength has improved over the years. Unless there is some real anomaly with the scale design, there should be no problem staying within the proportional limit of the strings. Besides, there is nothing that you can do about it, short of redesigning the bridge. It changes with the wire gauge: If you decrease the wire gauge, you decrease the tension and the proportional limit. The only place it would be a problem is with the bass strings, and that is up to the bass string designer.

I just ran some scenerio comparisons for the 1906 Crown upright originally engineered at A435 with the "Calculating Technician" spreadsheet by Dave Roberts (converted to excel by Douglas K. Rhodes, RPT).

They state that the three critical factors are, in priority, Volume; Breaking point; and Inharmonicity.

What I found was that in the string range #27 to 88, when the original string dimension range #18 down to #12 wire was tuned up from A435 to A440, that the volume decreased by almost 50% -- primarily in the #27 to #37 keys, as they transition to the bass section.

When I expanded the wire diameter range going from #22 down to #12 the pattern of volume replicated the original chart, but with the only difference being the pitch, as I converted to A440.

I tried to post the three charts on this BBS (original strings at A435, original strings at A440, and new broader string range at A440) but could not figure out how to do it.

If anyone is interested I can send it to you in a word document, just e-mail me.

Volume range on the first chart (original strings, A435) is from about 260 to 120.

Volume range on the second chart (original strings, A440) is from about 150 to 120.

Volume range on the third chart (expanding new strings from original #18-#13 up to #22-#12 at A440) is again from about 260 to 120 like the original chart.

Keeping the string range the same, the volume gap increased between the bass section as volume decreased -- the change narrowed the volume difference between the bass section and treble making it a smoother transition.

Tension, breaking point, and inharmonicity all remained within parameters on all three charts.

I did find someone who is winding the new bass strings in Canada in Iron instead of copper, like the original. He double-winds and says the bass will be "booming." He had to order the iron wire from England. The first ten strings are copper-wound. Starting at #18 in the treble section, together with a timid single-wound copper bass section may be appropriate, but I am taking painstaking measures on this piano, which is in some ways somewhere between an exact restoration, and a renovation to modern. "Same sound but modern key." I want Debussy to send shivers up your spine, and lift you up to the top of a spire of a cathedral!

I have studied this entire thread and attempted to re-scale a 1949 Lester 6'2" grand using the spreadsheet of BDB and input from Bill Bremmer RPT as they attempted to assist Ryan Marlowe.

In the past, I have replaced many broken wires, and have replaced full sets of wound bass strings, but am now attempting to help a beloved aunt restore her grand piano to "better than new" condition. I am not certain, but believe the piano may have been restrung before. The original wires measured from 18 to 12 1/2.

Using the spreadsheet, I added my measurements and then tried to "tweak" the wire sizes to attain as close to a uniform 160 pounds across the scale. I ended up with a scale ranging from 156 to 165 pounds of tension.

Am I on the right track, or am I missing something here ?I will appreciate any opinions or criticism !!

"Volume range on the first chart (original strings, A435) is from about 260 to 120.

Volume range on the second chart (original strings, A440) is from about 150 to 120."

Any explanation to this counter intuitive fact ?

more tension mean less iH and more elasticity, how does it relates to volume ? I have the Travis book but did not remind the way he compute volume, it should be related to mass and tension, and I see no reason it lower with more tension, unless it is about the harmonic content and that volume is only the first partial (?)

Edited by Olek (02/07/1310:44 AM)

_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills

If you have a fixed speaking length, in order to increase the tension, you have to increase the diameter of the string, which increases the inharmonicity. Assuming that you want to tune each note to pitch, of course!

It is a little difficult to get but if you increase the diameter of course, you get more iH but if you change the pitch your raise the elasticity of the wire then the iH lowers. Call that anything, it seem like elasticity (faster return to original dimension in cas eof deformation)

So assuming you keep the same diameters and you raise the tension, why would the volume lower ? just because of less parsing of the partials ? Is not volume a global energy measure ? is it just for the fundamental ?In that case I can understand, as more partials mean less fundamental probably (?)

Edited by Olek (02/07/1301:13 PM)

_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills

BDB, the link to your spreadsheet seems to be broken (I know its an old thread ). If you would be willing to repost or email me (miscrmsATgmail.com) a copy I would be very interested to play around with it. Probably won't be restringing any pianos any time soon, but its very interesting stuff!

Also noticed the local library has the Travis book mentioned, so I'll have to swing by sometime and pick that up unless there's something better/more recent you all would recommend.

An un-even number of unisons of any given gauge always calls for a tied off string. In most pianos, tied strings occur only at a few special places. For the vast part, there are even numbers of unisons of a given gauge, which allows for the string to loop around the hitch pin and come back to the next tuning pin.

Unless you begin to pull out hitch pins, and drill holes for new ones, you will not have the luxury of plopping any given spreadsheet-generated scale onto an existing piano plate.

Remember: piano design is all about compromise (in the right spots, of course)

I have studied this entire thread and attempted to re-scale a 1949 Lester 6'2" grand using the spreadsheet of BDB and input from Bill Bremmer RPT as they attempted to assist Ryan Marlowe.

In the past, I have replaced many broken wires, and have replaced full sets of wound bass strings, but am now attempting to help a beloved aunt restore her grand piano to "better than new" condition. I am not certain, but believe the piano may have been restrung before. The original wires measured from 18 to 12 1/2.

Using the spreadsheet, I added my measurements and then tried to "tweak" the wire sizes to attain as close to a uniform 160 pounds across the scale. I ended up with a scale ranging from 156 to 165 pounds of tension.

Am I on the right track, or am I missing something here ?I will appreciate any opinions or criticism !!

Many thanks,ncpianoman

As I see it the stretch of the wire is important too, hence the BS relation hich is not only there as a security, but as a tone quality parameter. But first tension of course (while on old pianos the tension curve (never find a flat tension scheme) is lowering in the high treble, while in modern ones it raise.

We could say that the yeld stretch is raised in the treble region, to compensate for our human ear that hear less good that frequency range. So the raise in tension as well as in stretch seem a good reason. it also fight the iH rise

_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills

I just ran some scenerio comparisons for the 1906 Crown upright originally engineered at A435 with the "Calculating Technician" spreadsheet by Dave Roberts (converted to excel by Douglas K. Rhodes, RPT).

They state that the three critical factors are, in priority, Volume; Breaking point; and Inharmonicity.

What I found was that in the string range #27 to 88, when the original string dimension range #18 down to #12 wire was tuned up from A435 to A440, that the volume decreased by almost 50% -- primarily in the #27 to #37 keys, as they transition to the bass section.

When I expanded the wire diameter range going from #22 down to #12 the pattern of volume replicated the original chart, but with the only difference being the pitch, as I converted to A440.

I tried to post the three charts on this BBS (original strings at A435, original strings at A440, and new broader string range at A440) but could not figure out how to do it.

If anyone is interested I can send it to you in a word document, just e-mail me.

Volume range on the first chart (original strings, A435) is from about 260 to 120.

Volume range on the second chart (original strings, A440) is from about 150 to 120.

Volume range on the third chart (expanding new strings from original #18-#13 up to #22-#12 at A440) is again from about 260 to 120 like the original chart.

Keeping the string range the same, the volume gap increased between the bass section as volume decreased -- the change narrowed the volume difference between the bass section and treble making it a smoother transition.

Tension, breaking point, and inharmonicity all remained within parameters on all three charts.

Hello thanks for chiming in, any reason why the volume should lower with more tension ? (435 to 440 ?)

Older wire could have alower breaking strain and can be tense more in the good constrain one with less tension.Modern wire oblige to make much compromizing as it is more hard. I have seen numerous old instruments that had definitively lost their original tone because of new strings.SOme colleagues even keep the old wire find in some old Erards going to dump, so they can keep the original wire. I never heard a modern replacement with such a tone quality.

On the contrary, unless you have along enough scale you are in trouble with older designs.

Some reasearch pretend than the old wire had phosphorous traces and that this is why the tone was so particular. Today no string maker will accept to have phosphorous in their batches so we cannot have that done again.

_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills

I believe that the wire sollicitation is taken in account in order to keep the stretch of the wire in correspondence with the frequencies, then the piano cna stay in tune longer.

in the mediums , where the soundboard change are the most noticeable, is suppose that a maximum of tension is also expected so to limit tone changes with the soundboard shape changes.It does not happen really with old panels so this may not be a problem.

Anyway low level of solicitation provide that flacid tone with proeminent partials and too much iH, that can be noticed on some old pianos stringed with modern wire, it is sensitive with american wire in the treble of a Steinway I have seen lately, that treble is all but elegant (5th octave) . did not check the wire diameters but I can hear the lack of solicitation there, because I am acustomed to that kind of flaws in the tone on old pianos.

Moaning a lot and difficult to make a nice tone with tuning; Harsh, give an impression of power but non musical one, When you voice down the tone get just more accepteable.

too much iH = the spectra is unclear the fundamental is perturbated, pitch refernce is not evident.

_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills

This is exactly the information I needed to hear ! SO, if I understand correctly, I should make adjustments to my "tweaked" scale, to a "final" scale using even numbers of unisons while still attempting to retain the most even pounds of tension, right ?

What about the post by Oleg ? Should I attempt to raise the tension in the treble in a smooth curve toward a certain tension in the treble ? What would be that ultimate tension on note 88 ? And, if so, at which note should I begin that upward curve ?

I try to keep note 88 close to 160 lb. The problem is the transition from the highest wound note to the lowest plain note. You could plug in the diameter of the highest wound note to get an approximation of the tension on that string. It has to be converted to a gauge. The conversion factor that I use on the spreadsheet is that the diameter in thousands minus 5 divided by 2 is the gauge. So for .031 inch diameter, that is (31 - 5)/2 = 13 gauge. That conversion works for the usual gauges used in pianos, but it is not accurate for much smaller and larger gauges.

This is exactly the information I needed to hear ! SO, if I understand correctly, I should make adjustments to my "tweaked" scale, to a "final" scale using even numbers of unisons while still attempting to retain the most even pounds of tension, right ?

What about the post by Oleg ? Should I attempt to raise the tension in the treble in a smooth curve toward a certain tension in the treble ? What would be that ultimate tension on note 88 ? And, if so, at which note should I begin that upward curve ?

I truly appreciate all this kind and helpful assistance from ALL !!

ncpianoman

Hello NCP, if you have an even tension you cannot really be wrong at the base, what I refer to is the level of solicitation the wire is subjected to. AN accepted rule is to avoid too low levels (the computing in Europe differs from the way it is seen in the Travis book , as a security 25% lowering is used on the real breaking strenght before computing how much % is allowed)

This to take in account "at large" the fragility induced by bends and coils.

Then not less than 40% in the first plain notes, raising to 80% BS in the last treble notes, and you have aneat moderate scale.

Original tension in many old scale make a hop on the first 10 notes then lowers sligthly toward the high treble.SO if you can raise it possibly you will have a better result in the end, as modern wire ask more tension to tone well than the one availeable at older times (in my opinion)

so in the mediums, the goal is to have around 50-60% solicitation. It is just that the mechanical behaviour of the wire is better in those limits, and can raise with thinner wire. The optimum tone for treble being not far from the end of the elastic zone of the wire.

Recent proposals from Paulelo, that are pplied with good results whatever wire is used. I also know at lat one manufacturer that use more solicitation even in the mediums, and I also have senn thos high levels of BS attained in the mediums by some old high tension scales (Pleyel, 1915)

But for instance Bechstein pianos of today have a little tension in the low mediums that raise toward the treble...

You have differnt types of scale, it should be interesting to determine what kind of scale your instrument had, as it may relate with the resiliency and the weight of your soundboard.

The last being now old, some corrections can be envisaged so you dont ask too much of the panel...

What helps to ascertain the scale is a comparison of the string's lenght progressiveness on a spreadsheet in logarithm display mode :the original frequency (f) in HZ, multiplied by the string length (speaking length) in meter

(direct display of the lenght give not as much information)

You can see where the lenght reduction begin on the scale, how is the bottom of the long bridge.